- Home
- Best Scientists - Mathematics
- George Em Karniadakis

Mathematics

USA

2023

Mechanical and Aerospace Engineering

USA

2023

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mechanical and Aerospace Engineering
D-index
99
Citations
45,386
547
World Ranking
31
National Ranking
20

Mathematics
D-index
114
Citations
59,170
667
World Ranking
9
National Ranking
6

2023 - Research.com Mathematics in United States Leader Award

2023 - Research.com Mechanical and Aerospace Engineering in United States Leader Award

2018 - Fellow of the American Association for the Advancement of Science (AAAS)

2013 - THE J. TINSLEY ODEN MEDAL For outstanding contributions to stochastic differential equations, in particular modelling uncertainty with polynomial chaos and development of spectral and hp element methods on unstructured meshes

2011 - ACM Gordon Bell Prize For "A new computational paradigm in multiscale simulations: Application to brain-blood flow."

2010 - SIAM Fellow For contributions to stochastic modeling, spectral elements, and fluid mechanics.

2007 - THE THOMAS J.R. HUGHES MEDAL

2004 - Fellow of American Physical Society (APS) Citation For his innovative developments and his insightful applications of the spectralelement method in computational fluid dynamics

2002 - Fellow of the American Society of Mechanical Engineers

- Quantum mechanics
- Mathematical analysis
- Statistics

Mechanics, Mathematical analysis, Classical mechanics, Reynolds number and Applied mathematics are his primary areas of study. His Mechanics study frequently draws connections between related disciplines such as Cylinder. His biological study spans a wide range of topics, including Stochastic process and Monte Carlo method, Polynomial chaos.

The concepts of his Classical mechanics study are interwoven with issues in Dissipative particle dynamics, Heat transfer, Hele-Shaw flow, Direct numerical simulation and Flow visualization. His Reynolds number research incorporates elements of Flow, Navier–Stokes equations, Laminar flow and Amplitude. The various areas that George Em Karniadakis examines in his Applied mathematics study include Galerkin method, Nonlinear system, Compressibility, Mathematical optimization and Discretization.

- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (3207 citations)
- High-order splitting methods for the incompressible Navier-Stokes equations (1126 citations)
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (1079 citations)

His scientific interests lie mostly in Mechanics, Mathematical analysis, Applied mathematics, Classical mechanics and Flow. As part of his studies on Mechanics, George Em Karniadakis often connects relevant areas like Dissipative particle dynamics. His studies in Dissipative particle dynamics integrate themes in fields like Mesoscopic physics and Hagen–Poiseuille equation.

His Mathematical analysis research is multidisciplinary, incorporating perspectives in Stochastic process and Polynomial chaos. His Applied mathematics study integrates concerns from other disciplines, such as Artificial neural network, Mathematical optimization and Nonlinear system. His Artificial neural network research integrates issues from Algorithm, Deep learning, Partial differential equation and Inverse problem.

- Mechanics (24.00%)
- Mathematical analysis (14.29%)
- Applied mathematics (13.73%)

- Artificial neural network (9.82%)
- Applied mathematics (13.73%)
- Inverse problem (4.24%)

George Em Karniadakis focuses on Artificial neural network, Applied mathematics, Inverse problem, Artificial intelligence and Nonlinear system. His Artificial neural network research is multidisciplinary, relying on both Uncertainty quantification, Algorithm and Partial differential equation. His Applied mathematics research incorporates themes from Operator, Boundary value problem, Space, Discretization and Function.

His research in Inverse problem intersects with topics in Acoustics, Euler equations, Inverse, Finite element method and Hyperparameter. His Artificial intelligence research is multidisciplinary, incorporating elements of Machine learning and Physical law. His work on Nonlinear system is being expanded to include thematically relevant topics such as Conservation law.

- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (1079 citations)
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. (158 citations)
- Deep learning of vortex-induced vibrations (103 citations)

- Quantum mechanics
- Statistics
- Artificial intelligence

His primary scientific interests are in Artificial neural network, Applied mathematics, Nonlinear system, Artificial intelligence and Deep learning. George Em Karniadakis has included themes like Algorithm, Partial differential equation and Inverse problem in his Artificial neural network study. His research integrates issues of Domain decomposition methods, Space, Discretization, Function and Domain in his study of Applied mathematics.

George Em Karniadakis does research in Nonlinear system, focusing on Burgers' equation specifically. His study looks at the relationship between Finite element method and fields such as Navier–Stokes equations, as well as how they intersect with chemical problems. George Em Karniadakis combines subjects such as Stochastic differential equation and Mathematical optimization with his study of Stochastic process.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Dongbin Xiu;George Em Karniadakis.

SIAM Journal on Scientific Computing **(2002)**

4994 Citations

Spectral/hp Element Methods for Computational Fluid Dynamics

George Karniadakis;Spencer J. Sherwin.

**(2005)**

3203 Citations

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Maziar Raissi;Paris Perdikaris;George E. Karniadakis.

Journal of Computational Physics **(2019)**

2972 Citations

Microflows and Nanoflows: Fundamentals and Simulation

George E Karniadakis.

**(2008)**

2486 Citations

The Development of Discontinuous Galerkin Methods

Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu.

**(2000)**

2065 Citations

High-order splitting methods for the incompressible Navier-Stokes equations

George Em Karniadakis;Moshe Israeli;Steven A Orszag.

Journal of Computational Physics **(1991)**

1722 Citations

Modeling uncertainty in flow simulations via generalized polynomial chaos

Dongbin Xiu;George Em Karniadakis.

Journal of Computational Physics **(2003)**

1595 Citations

Spectral/hp Element Methods for CFD

George Em Karniadakis;Spencer J Sherwin.

**(1999)**

1409 Citations

REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES

Ali Beskok;George Em Karniadakis.

Microscale Thermophysical Engineering **(1999)**

1340 Citations

Discontinuous Galerkin Methods: Theory, Computation and Applications

Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu.

**(2011)**

960 Citations

If you think any of the details on this page are incorrect, let us know.

Contact us

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

University of Pennsylvania

MIT

Imperial College London

Brown University

University of Utah

Nanyang Technological University

The Ohio State University

Brown University

Southern Methodist University

Shaanxi Normal University

University of Bath

Kunming University of Science and Technology

University of Warwick

Max Planck Society

Osaka University

Swinburne University of Technology

Institut Gustave Roussy

Mayo Clinic

McGill University

Swansea University

University of Guelph

University of California, San Francisco

University of Minnesota

Johns Hopkins University

The University of Texas at Austin

Something went wrong. Please try again later.